Question

adow
straight - line distance from the top of the tower to
40° angle with the ground. what is the approximate
to the nearest whole number?
(there is a right - triangle diagram with one angle 40°, the vertical side labeled tower with length 52 m, the horizontal side labeled shadow, and the hypotenuse is what we need to find, denoted as x. at the bottom, it says x = ______ m)

Explanation:

Step1: Identify the trigonometric ratio

We have a right triangle where the opposite side to the \(40^{\circ}\) angle is the height of the tower (\(52\) m) and the adjacent side is the length of the shadow (\(x\)). The tangent function relates the opposite and adjacent sides: \(\tan(\theta)=\frac{\text{opposite}}{\text{adjacent}}\). So \(\tan(40^{\circ})=\frac{52}{x}\).

Step2: Solve for \(x\)

Rearrange the formula to solve for \(x\): \(x = \frac{52}{\tan(40^{\circ})}\). We know that \(\tan(40^{\circ})\approx0.8391\). Then \(x=\frac{52}{0.8391}\approx62\) (rounded to the nearest whole number).

Answer:

\(62\)